This study investigates the supply chain inventory problems when the supply price increases and market demand rate depends on retail price. The purpose of this study will be to determine optimal special order quantity, retail price and production cycle by maximizing the increment of joint total profit. Furthermore, due to the vendor may or not provide all the special order quantity at the buyer’s next replenishment date and hence the shortage will or not occur, two specific situations are discussed in this study. A simple algorithm to find the optimal solution is developed. Finally, several numerical examples will be presented to demonstrate the developed model and solution procedure to provide manager a useful decision consultation.
